Given a vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a field of projective forces, we define a law of dynamics such that the position of the particle is a ray i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is a 2-plane containing the ray. Throwing the particle with a given initial impulsion def...

‎let us consider the set of non-abelian finite simple groups which‎ ‎admit non-trivial irreducible projective representations of degree $le 7$ over‎ ‎an algebraically closed field $f$ of characteristic $pgeq 0$‎. ‎we survey some recent results which‎ ‎lead to the complete list of the groups in this set which are‎ ‎$(2‎, ‎3‎, ‎7)$-generated and of those which are $(2,3)$-generated‎.

‎let us consider the set of non-abelian finite simple groups which‎ ‎admit non-trivial irreducible projective representations of degree $le 7$ over‎ ‎an algebraically closed field $mathbb{f}$ of characteristic $pgeq 0$‎. ‎we survey some recent results which‎ ‎lead to the complete list of the groups in this set which are‎ ‎$(2,3,7)$-generated and of those which are $(2,3)$-generated‎.

Let X/S be a quasi-projective morphism over an affine base. We develop in this article a technique for proving the existence of closed subschemes H/S of X/S with various favorable properties. We offer several applications of this technique, including the existence of finite quasi-sections in certain projective morphisms, and the existence of hypersurfaces in X/S containing a given closed subsch...

let $g$ be a group and $mathcal{n}$ be the class of all nilpotent groups. a subset $a$ of $g$ is said to be nonnilpotent if for any two distinct elements $a$ and $b$ in $a$, $langle a, brangle notin mathcal{n}$. if, for any other nonnilpotent subset $b$ in $g$, $|a|geq |b|$, then $a$ is said to be a maximal nonnilpotent subset and the cardinality of this subset (if it exists) is denoted by $ome...

Let C be a smooth, projective and geometrically connected curve defined over finite field

Any free presentation for the finite group G determines a central extension (R, F ) for G having the projective lifting property for G over any field k. The irreducible representations of F which arise as lifts of irreducible projective representations of G are investigated by considering the structure of the group algebra kF , which is greatly influenced by the fact that the set of torsion ele...

Given the algebra T of ternions (upper triangular 2× 2 matrices) over a commutative field F we consider as set of points of a projective line over T the set of all free cyclic submodules of T 2. This set of points can be represented as a set of planes in the projective space over F 6. We exhibit this model, its adjacency relation, and its automorphic collineations. Despite the fact that T admit...

known as the left big finitistic projective dimension of A, is finite. Here pdM denotes the projective dimension of M . Unfortunately, this number is not known to be finite even if A is a finite dimensional algebra over a field, where, indeed, its finiteness is a celebrated conjecture. On the other hand, for such an algebra, finite flat certainly implies finite projective dimension, simply beca...